MSI Friends and Alumni: Playing the Chaos Game

Professor Michael Barnsley will be presenting a special lecture for MSI's Alumni, friends and colleagues. The presentation will be followed by drinks, hors-d’oevres and a chance to meet and chat with the speaker and other members of the MSI. 

Attendance at these special lectures is by invitation only, so if you would like to attend, please register as a friend of MSI to receive your invitation. 


The chaos game is a key to solving many interesting problems. Mark three non collinear points on a sheet of paper. Label them A, B and C. Let an infinite sequence S=ABAACCBABABBACCBAC…. contain all 'words' that can be made from the 'alphabet'  {A,B,C}. Let S(n) be the nth member of S. Choose X(0) at random on the paper. Define and plot an infinite sequence of points in the plane (on the paper) by X(n+1)=(S(n)+X(n))/2. The result will eventually be a 'picture' of the Sierpinski triangle with vertices at A, B and C. Figure 1 illustrates the ideas.

Chaos game on a Sierpinski triangle

Figure 1: Chaos game on a Sierpinski triangle

Recent advances in understanding this  simple algorithm in very general setttings will be described in elementary terms. The talk will include pictures, references to fairy tales, and an application using 3-D  printing.

About the speaker

Michael Barnsley has a B.A. from Oxford University and a PhD from the University of Wisconsin. In previous lives he was a child of a poet, an itinerant post-doc in Europe, and a professor at Georgia Tech. He is well known for developing fractal image compression. He is currently researching three-dimensional fractal transformations under a grant from the ARC.

Date & time

5.30–8pm 28 February 2013


Copland Theatre, Building 25


Michael Barnsley


 Brittany Shoard
 6125 2897

Updated:  26 September 2017/Responsible Officer:  Director/Page Contact:  School Manager